Regular Generalized<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="E1"><mml:mi>ω</mml:mi></mml:math>-Closed Sets

Abstract

In 1982 and 1970, Hdeib and Levine introduced the notions of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="E2"><mml:mi>ω</mml:mi></mml:math>-closed set and generalized closed set, respectively. The aim of this paper is to provide a relatively new notion of generalized closed set, namely, regular generalized<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="E3"><mml:mi>ω</mml:mi></mml:math>-closed, regular generalized<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="E4"><mml:mi>ω</mml:mi></mml:math>-continuous,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="E5"><mml:mi>a</mml:mi></mml:math>-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="E6"><mml:mi>ω</mml:mi></mml:math>-continuous, and regular generalized<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="E7"><mml:mi>ω</mml:mi></mml:math>-irresolute maps and to study its fundamental properties.